Based on discussions on twitter, it seems pretty clear that a lot of Non-PI scientists don't really understand the concept of indirect costs, aka overhead. Most people know that a university's overhead rate is what they take from federal grant dollars to "keep the lights on", so to speak. But how is it calculated and how is it spent?
The indirect rate is something each university negotiates with the federal government. So, when someone tells you their overhead rate is 51%, that the number their university has worked out with the feds. The rates for NSF, DoD and NIH are always the same, USDA and (I think) NASA are lower. That's a discussion for another time. Now, a rate of 51% does not mean half your grant goes into the dark cauldron of university expenses. Overhead is calculated by taking the total of adjusted* direct costs and finding the 51% of that number and adding it to the total direct costs.
So, if your adjusted direct costs are $100k, the overhead on that will be $51k. If, once you add tuition and equipment in, your total direct costs are $120K, the total budget will be $171k. In this hypothetical case, the overhead amount on the grant is only about 30% of the total budget. NIH applicants only ever deal with their direct costs in a budget (ie, NIH budget limitations, inasmuch as the exist, are on direct costs only, not total budget), but everyone else calculates the total budget.
Ok, so now that we have calculated overhead and you were awarded the grant, what happens to all that money? Well, it doesn't get freed up into the coffers until you spend money off your grant. For every dollar you spend, fifty-one cents of overhead money gets it's wings. As you spend, the university gets cash.
Most of that cash will find it's way directly into the university-level machine. Somewhere in the neighborhood of 70-80% will get gobbled up right away, with the rest landing next in your college. Your college will take a giant bite out of that (usually at least 50%), before your department gets to swing the bat. Different departments do it differently, and I've seen situations where the department takes everything that remains, whereas others return all of the overhead back to the investigator. Usually the solution is somewhere in between, so let's say that 50% goes to the department and 50% goes to the PI.
The PI is allowed to use that money to do things like cover shipping, buy software and journal subscriptions, bring in people for interviews for lab positions, cover salary, etc. In many places, this is a very useful, if small, pot of money to have available. However, overhead generated on a particular project should, by law, be expended entirely by the end of that project. In practice, this is almost impossible, but stockpiling overhead money to CYA later is heavily frowned upon.
What the university and college do with the overhead money varies, but much of it is related to supporting costs of the research enterprise (think, compliance, university vet, grants staff, etc.). Additionally, those monies are often used as part of start-up packages for new hires, meaning a lean year for indirects directly effects the hiring and recruitment process.
* Some things like equipment and tuition are non-overhead bearing budget lines, so they are subtracted from the total.